A leading American economist predicted yesterday that, with the help of the Japanese government, the yen will appreciate to a rate of 190 to the dollar within "the next month or two," leading to a significant reduction in its bilateral trade surplus with the United States by the second half of 1986.

C. Fred Bergsten, director of the Institute of International Economics, made that forecast at a press conference in conjunction with a report on U.S.-Japan problems that he co-authored with William R. Cline of the institute staff.

The main theme of the report, a preliminary version of which was published earlier this year, is that the $50 billion trade surplus Japan is expected to rack up against the United States this year can be traced almost entirely to the overvalued dollar.

It also says that the effects of Japanese protectionism on the trade imbalance have been seriously exaggerated and, in fact, are barely more serious than American barriers against Japanese imports. "The centerpiece of the [necessary] policy package to deal with the U.S.-Japan trade conflict must be a determined effort to reduce the U.S. fiscal deficit," the Bergsten-Cline report concluded.

Bergsten said that there is "widespread acceptance" among the Japanese authorities of the need to bring the value of the yen at least to 200 to the dollar, and that many officials and businessmen see the need to go to 190 to 1, or even 180 to 1 from the present approximate level of 215 to 1.

In an interview last week in New York, Prime Minister Yasuhiro Nakasone acknowledged that government policy is to "strengthen the yen further." He would not mention a target figure. Former foreign minister Saburo Okita, after a meeting with Bergsten and other economists on the foreign exchange issue, said last week that the government was aiming at a 200-to-1 ratio.

A new rule of thumb offered in the Bergsten-Cline report is that, for every 10 percent change in the yen-dollar exchange rate, the bilateral balance changes by about $8.3 billion. Thus, if the yen should appreciate to 190 to 1 -- a move of 20 percent from the 240-to-1 level prevailing before coordinated intervention was begun on Sept. 22 -- the reduction in the U.S. trade deficit would be about $17 billion.

Bergsten said yesterday that the 190-to-1 ratio could be maintained for at least six months or longer even without the desired shift in underlying macroeconomic policy "because there has been a clear change in [intervention] policy by both governments. If they continue intervention, the markets will get tired of testing" the rate.

He added that there would be "a stronger basis" for durability of a 190-to-1 exchange rate if the Federal Reserve Board lowers interest rates, and if financial markets perceive the imminent passage of the Gramm-Rudman budget-balancing proposal as a real forerunner of major slashes in the budget deficit.

In seeking additional ways of reducing the Japanese trade surplus, the report said that the most that could be achieved from elimination of Japanese trade barriers, "both overt and intangible," was $5 billion to $8 billion. Another $3 billion to $7 billion might be picked up from elimination of controls on exports of Alaskan oil to Japan and from a speedup of Japanese economic growth.

That would reduce the Japanese bilateral trade surplus with the United States to about $20 billion to $25 billion, which the authors said was "the likely equilibrium level," or normal for a country such as Japan that has large deficits with oil-exporting and commodity-producing countries, and surpluses with other nations that buy its manufactured goods.

"It isn't realistic to think of getting the $50 billion [U.S. trade deficit with Japan] down to zero," Cline said. "If we see figures like $25 billion, we ought to declare victory, and abandon protectionist solutions."